II.—Investigation of an Expression for the Mean Temperature of a Stratum of Soil, in Terms of the Time of Year.

Extract

1. It is a well-known property of simple harmonic functions, that the sum of any two or more of them having the same period, is itself a simple harmonic function having the same period as its components. The same thing must be true of their mean, since this is equal to the sum divided by a constant; and it will still be true when the number of components is indefinitely great, and the mean becomes an integral.